Scalar potential model of redshift and discrete redshift

On the galactic scale the universe is inhomogeneous and redshift z is occasionally less than zero. A scalar potential model (SPM) that links the galaxy scale z to the cosmological scale z of the Hubble Law is postulated. Several differences among galaxy types suggest that spiral galaxies are Sources and that early type, lenticular, and irregular galaxies are Sinks of a scalar potential field. The morphology-radius and the intragalactic medium cluster observations support the movement of matter from Source galaxies to Sink galaxies. A cell structure of galaxy groups and clusters is proposed to resolve a paradox concerning the scalar potential like the Olber's paradox concerning light. For the sample galaxies, the ratio of the luminosity of Source galaxies to the luminosity of Sink galaxies approaches 2.7 ± 0.1. An equation is derived from sample data, which is anisotropic and inhomogeneous, relating z of and the distance D to galaxies. The calculated z has a correlation coefficient of 0.88 with the measured z for a sample of 32 spiral galaxies with D calculated using Cepheid variable stars. The equation is consistent with z < 0 observations of close galaxies. At low cosmological distances, the equation reduces to z ≈ exp(KD)−1 ≈ KD, where K is a constant, positive value. The equation predicts z from galaxies over 18 Gpc distant approaches a constant value on the order of 500. The SPM of z provides a physical basis for the z of particle photons. Further, the SPM qualitatively suggests the discrete variations in z, which was reported by Tifft [Tifft, W.G., 1997. Astrophy. J. 485, 465] and confirmed by others, are consistent with the SPM.